Conventionally, methods for structural optimization include dimensional optimization, shape optimization, and topology optimization.
Among the above conventional structural optimization methods, shape optimization obtains an optimum structure by using an outer shape as a design variable and updating the outer shape on the basis of sensitivity information, and is widely used in mechanical industries as a practical method.
However, a shape optimization method has an inherent disadvantage, namely, that a change in topology, i.e., a change in the number of holes in an optimum structure, cannot occur, and therefore significant improvement of structural performance cannot be expected.
On the other hand, topology optimization enables the topology of an optimum structure to be changed, by replacing an optimal design problem by a material distribution problem that, when solved, can be expected to provide significant improvement of structural performance.
However, a topology optimization may give rise to a numerical instability problem such as the inclusion of grayscale areas in the optimum structure, namely, areas that are not clearly specified as material or void, which degrades the utility and manufacturability of an obtained optimum structure.
Also, in recent years, as a new structural optimization method, structural optimization based on a level set method, has been proposed (Non-patent Literature 1).
In a level set-based topology optimization method, the outer shape of a structure is represented by a one-dimensional high-level level set function, and a change in shape and configuration is replaced by a change in the level set function value, so as to obtain an optimum structure. On this basis, a level set-based topology optimization method has the advantage of, differently from a conventional topology optimization method, being able to constantly and clearly represent the outline of an optimum structure, and it thereby avoids the occurrence of the numerical problem that leads to the inclusion of grayscale areas.
However, a typical level set-based topology optimization method updates the level set function on the basis of an advection equation, and is therefore based on the assumption that a change in topology (i.e., a change in configuration) such as the introduction of a hole in the material domain is not allowed.
On the other hand, as described in Non-patent Literature 2, a method has been proposed that, during the process of the structural optimization based on the level set method, on the basis of the topological derivatives of an objective function, appropriately introduces a hole, or holes, into the material domain in an arbitrary manner. Also, as described in Non-patent Literature 3, a method has been proposed that, during the optimization process, can replace a material domain (i.e., a domain where a structure is formed), which has a value of a topological derivative equal to a predetermined threshold value, by a void domain (i.e., a domain where a void is formed), and therefore this method allows a change in topology (i.e., a change in configuration) such as the introduction of a hole in the material domain.
However, all of the above-mentioned level set-based topology optimization methods have a problem of being highly dependent on parameter settings, such as the number of holes set in the initial configuration prior to optimization, or the setting of threshold values, and unless such parameters and values are appropriately set, these methods are unable to obtain a physically valid optimum structure (see Non-patent Literature 4).